Unit 2: The Atom

Half- Life

Half Life

The time required for one half of the nuclei of a radioactive isotope sample to decay to atoms of a new element.

Half-lives can range from a fraction of a second to billions of years..

Ex) Half-life of 90Sr is 29 years. If you had 10.0g of 90Sr today, in 29 years how much would remain?

Answer: 5.00g

Half-life Continued.

After each half-life, only half of the sample remains

Radioactive isotopes will decay until negligible amounts are present.

Calculating Half-life

Amount remaining = (initial amt) x (1/2)n

n = Total Time passed

Length of one half-life

Where n = the number of half life cycles that have passed.

Problem

59Fe is used in medicine to diagnose blood disorders. The half-life of 59Fe is 44.5 days. How much of a 2.00g sample will remain after 178 days?

n= 178/ 44.5n=4

amt remaining = (2.00) x (1/2)4

amt remaining= 0.125g

Example #2 Nitrogen-13 decays to Carbon-13 and the half-

life is 10 minutes. If you start with 2.0 grams of N-13, how many grams of N-13 will be left after 30 minutes have passed?

t ½ = 10 mins Start Amt = 2.0 g Total time passed = 30mins

Using the formulas

n = total time / half life = 30min / 10min = 3 half lives

Amt left = (2.0g) (½) 3 = (2.0) (½) (½) (½) = 0.25 g left.

Second Method – use a table

Time # half lives amount left

0 0 2.0 g

10 mins 1 1.0 g

20 mins 2 0.5 grams

30 mins 3 0.25 grams

Example #3

A 50 gram sample of nitrogen-16 decays to 12.5 grams in 14.4 seconds. What is the half-life of nitrogen –16?

# half lives past = total time or t1/2 = total time

t1/2 #half lives past

# half lives past Amt left

0 50g

1 25g2 12.5 g

t1/2 = 14.4 seconds

2

t1/2 = 7.2 seconds

Example 4

If 100 grams of Au-198 is left after 8.10 days and the half-life is 2.70 days, what was the original amount present?

# half lives past = total time t1/2

Amount remaining = (initial amt) x (1/2)n

100 g = (x) (1/2)3

= 8.10/2.7 = 3

X = 800 grams

= original amount